Actually there's more to abilities than just raw damage and abilities can be nerfed in ways that balance it without changing damage. You can nerf range, duration, radius, cooldowns, resource costs, and even cast time. If Riot had to balance just damage it wouldn't be so bad but there's way more variables than that.
For example let's look at: Morgana
At the moment she is still considered a strong pick although she recently dropped off competitive play a bit, I think she's still seeing play but a lot less than before the nerf.
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**Black Shield**
Base shield health reduced to 70/140/210/280/350 from 95/160/225/290/355.
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** Soul Shackles**
Base magic damage reduced to 150/225/300 from 175/250/325.
Total possible magic damage per target reduced to 300/450/600 from 350/500/650.
These were the nerfs and direction Riot chose to take but there is definitely alternate ways to nerf a champion. For example they could of nerfed the duration of her Black Shield from 5 seconds to 3 seconds, meaning you have to be more timely with Black shields as well as adds a counterplay window.
Her Q which is a 3 second duration (few abilities still have 3 seconds) is always brought up from time to time, as well as the hitbox of the Dark Binding. So, yes they could fix the hitbox which essentially nerfs it by making it easier to dodge. They could also nerf the duration to 2 seconds but lower the cooldown so you can use it more often but it's less of a game winning bind situation and requires your team to follow up in a more effective manner, but right now it's very forgiving because it's 3 seconds of reaction time to capitalize on.
They could even decrease the tether time on her ult which would buff that ability to compensate for a second off her Q duration. So Morg hits a Q and it now only lasts 2 seconds but then she walks up and ults but only has to wait 2 seconds before her ult does the 2nd portion damage + root. Making it easier for her to combo but less problems with just a single game winning bind.
There is plenty of ways for Riot to nerf champions without nerfing damage and yet still the majority of nerfs are damage and resource costs/cooldowns not to say that those don't work but sometimes I feel there are better directions and sometimes you need to nerf more than just damage.
I am however NOT a game designer or balance expert, all I have is years of experience playing and thinking about games. Also this is just a quick example because I know if you don't post quickly on these forums it hardly gets read.
